The research of the conversion and the relationship between each quotient space are important contents of the quotient space theory. Finer and coarser granularity quotient space can be obtained by conducting the infimum and supremum combination on the domain of some given quotient space. The relationship between the infimum and the supremum combination of domain is discussed. The relationship between the three types of quotient space is researched by defining the conception of the bonding mapping. The conditions are proposed and proved that, for any two quotient space ??1 and ??2 of the given original space, ??2 is the quotient space of ??1. The theoretical system of granular computing are enriched and improved further.